Solution:
we are given that
The population of a city in 2005 was 18000.
By 2010, the city’s population had grown to 45,000.
Economists have determined that the growth is exponential.
As we know the exponential growth is defined by the relation
[tex]P=p_0e^{rt}\\ \\ \text{where P is the population at time t and initial population is } p_0\\[/tex]
Here we have [tex]p_0=18000, P=45000, t=5[/tex]
substitute these values we get
[tex]45000=18000e^{5r}\\ \\ r=0.183[/tex]
So we get
[tex]P(t)=18000e^{0.183t}[/tex]
So For population is 2015 substitute t=10
[tex]P(10)=18000e^{0.183*10}[/tex]
[tex]P(10)=112209.9598 [/tex]
The projected population for 2015 is 112210
Robin earned $4,320 in 9 weeks and worked 40 hours in each week. How much did he earn per hour? $ per hour
Answer:
$12 per hour
Step-by-step explanation:
To solve how much did Robin earned per hour you just have to do a simple equation, we know that he worked 9 weeks, and that each week he worked 40 hours, so you equation would look like this:
[tex]Income=(wageperhour)*(hours worked)[/tex]
The hours worked is just a math done by multiplying the weeks worked by the hours worked per week that would be:
[tex]Hours worked=Hours worked per week*weeks\\Hours worked=(40 hours)*(9 weeks)\\Hours worked=360 hours[/tex]
So now we just put the data into our equation
[tex]Income=(wageperhour)*(hours worked)\\$4320=(wageperhour)*(360)\\wage per hour=4320/360\\ Wage per hour= 12[/tex]
Factor to find the zeros of the function defined by the quadratic expression. 16x2 − 240x + 896 A) x = 7 or x = 8 B) x = 7 or x = −8 C) x = −7 or x = 8 D) x = −7 or x = −8
Answer:
The correct answer is A).
Step-by-step explanation:
He have the quadratic functions f(x) = 16x²-240x+896. The first step should be to check if the coefficients 240 and 896 are divisible by 16, which is true. Then, extracting 16 as common factor we have
f(x) = 16(x²-15x+56).
Now we can use directly the formula to find the roots of a quadratic equation, or a more efficient way in terms of calculations. We must find to numbers such that their product is +56 and their addition or subtraction is -15. It is not difficult to check that -7 and -8 fulfill those conditions. Hence,
f(x) = 16(x²-15x+56)= 16(x-7)(x-8).
Therefore, the solutions are x=8 and x=7.
A model rocket is launched from the ground with an initial velocity of 40 feet per second. The height of an object h, in feet, after t seconds, with initial velocity v0v0 and initial height h0h0 is given by h(t)=−16t2+v0t+h0h(t)=−16t2+v0t+h0 .
What is the approximate maximum height the rocket reaches?
Enter your answer in the box.
ft
The approximate maximum height that the rocket reaches is 25 feet.
What is a function?
Function is a type of relation, or rule, that maps one input to specific single output. Given two function f(x) and g(x) can be written as f(X) + g(X). It is the sum of two functions similar to the addition of any two polynomial functions
+ x -7.
We are given that;
Initial velocity of the rocket= 40 feet per second.
The height of the rocket after t seconds is given by the formula:
h(t) = -16t^2 + v0t + h0
where v0 is the initial velocity (in feet per second) and h0 is the initial height (in feet).
Since the rocket is launched from the ground, its initial height is h0 = 0. Substituting this and v0 = 40 into the formula, we get:
h(t) = -16t^2 + 40t
To find the approximate maximum height that the rocket reaches, we need to find the vertex of the parabolic function h(t) = -16t^2 + 40t. The vertex occurs at the value of t that maximizes the height, which is given by:
t = -b/2a
where a = -16 and b = 40 are the coefficients of the quadratic function. Substituting these values into the formula, we get:
t = -40/(2*(-16)) = 1.25
Therefore, the rocket reaches its maximum height after approximately 1.25 seconds. To find the maximum height, we can substitute this value of t into the formula for h(t):
h(1.25) = -16(1.25)^2 + 40(1.25) ≈ 25 feet
Therefore, by the given function answer will be 25 feet.
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judy has $20 and is saving at a rate of $6 per week. Ida has $172 and spending at a rate of $4 per week. After how many weeks will each have the same amount?
please help me out due at 10
Is 18 T greater than 36,000 lb
use pi = 3.14 to estimate the circumference of the circle to the nearest hundredth.
middle of circle is 11cm
Answer:
Circumference of the circle to the nearest hundredth is, 69.08 cm
Step-by-step explanation:
Circumference(C) of the circle is given by:
[tex]C = 2\pi r[/tex] .....[1]
where,
r is the radius of the circle.
As per the statement:
middle of circle is 11 cm
⇒[tex]r = 11 cm[/tex]
use [tex]\pi = 3.14[/tex]
Substitute these in [1] we have;
[tex]C = 2 \cdot 3.14 \cdot 11 = 69.08 cm[/tex]
Therefore, the circumference of the circle to the nearest hundredth is, 69.08 cm
The circumference of a circle with a radius of 11cm is 69.08cm, rounded to the nearest hundredth.
To estimate the circumference of a circle using π (Pi), you need to know the diameter of the circle which is twice the radius. Since you've mentioned the circle has a middle (radius) of 11cm, the diameter is 22cm. The formula for the circumference of a circle is C = πd, where d is the diameter.
Using the given approximation of Pi (π = 3.14), you can calculate:
C = 3.14 × 22cm
C = 69.08cm
Therefore, the estimated circumference is 69.08cm, which can be rounded to the nearest hundredth as 69.08cm.
Which property is used in the problem below? 2(x+4)=2x+8 the associative property the commutative property the distributive property the additive identity property
Answer: I took a test, the answers C.
Step-by-step explanation:
If r=4 units and x = 8 units then what is the volume of the cylinder shown above use 3.14 for TT and round your answer to the nearest hundredth
Final answer:
The volume of a cylinder with a radius of 4 units and a height of 8 units is 401.92 cubic units, calculated using the formula V = πr²h and rounding to the nearest hundredth.
Explanation:
Calculating the Volume of a Cylinder
To find the volume of a cylinder, we can use the formula V = πr²h, where 'V' represents the volume, 'r' is the radius, and 'h' is the height of the cylinder. Since you have provided that the radius (r) is 4 units and the height (x) is 8 units, we can substitute these values into the formula as follows:
V = 3.14 × (4 units)² × 8 units
First, we calculate the radius squared (4 units)²:
(4 units)² = 16 units²
Now we multiply this by the height and π as given:
V = 3.14 × 16 units² × 8 units
V = 3.14 × 128 units³
V = 401.92 units³
Therefore, the volume of the cylinder is 401.92 cubic units, rounded to the nearest hundredth.
PLEASEE HELP ASAP WILL GIVE BRAINLIEST!!!
Answer:
The heat added to the system.
Step-by-step explanation:
Eight minus the quotient of two and a number X
Answer:
8 - 2/x
Step-by-step explanation:
All you have to do is read the problem and then you will get your answer so as you see it say 8 - ok you get that now when it say the the quotient of two that means it’s is 2 over x so like the 2/x
eight minus the quotient of two and a number x
Hoped I Helped
What is 5 and 4/5 plus 1 and 1/8? Please help. Thx
how many 1/8s in 25?
A number cube has six faces, numbered 1 to 6. John tossed two number cubes several times and added the numbers each time
John adds the outcomes of rolling two dice each showing numbers 1-6. In total, there are 36 possible outcomes when rolling two dice. The totals of the outcomes range from 2 to 12, with varying probabilities of each total.
Explanation:John's activity involves the mathematical operation of adding the outcomes of two number cubes, also known as six-sided dice. Each die has six faces, numbered from 1 to 6. When you roll two dice, there are 36 possible outcomes (6 options from the first die multiplied by 6 options from the second die).
For example, the dice could both show a 1, both show a 2, and so on up to 6. Alternatively, they could show different numbers, like 1 and 2, 1 and 3, up until 5 and 6. If you list all 36 possibilities and add up the numbers shown on the dice for each possibility, you'll get every total from 2 to 12.
Each total has a certain probability of occurring, based on how many of the 36 possibilities will result in that total.
For example, there's only one way to get a total of 2 (both dice showing 1), but there are several ways to get a total of 7 (1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, 6 and 1).Learn more about Probability here:https://brainly.com/question/22962752
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what is the area of this circle with a diameter of 3.7 inches
which stem-and-leaf plot represents the data 80, 81, 91, 92, 66, 55, 54, 30, 55, 79, 78?
key for picture one is Key: 5|0 means 50
pic 2 Key: 5|4 means 54
pic 3 Key: 5|4 means 54
pic 4 Key: 5|4 means 54
Answer:
d its d
Step-by-step explanation:
A rectangular prism has a lenght of 8 inches and a width of 7 inches. The lateral area is 150 square inches . What is the height of the prism?
If a rectangular prism has a lenght of 8 inches and a width of 7 inches. The lateral area is 150 square inches then the height of the rectangular prism is 5 inches.
To find the height of the rectangular prism, we'll first find the formula for the lateral area of a rectangular prism and then solve for the height using the given lateral area.
The lateral area of a rectangular prism is given by the formula:
[tex]\[ \text{Lateral Area} = 2 \times (\text{Length} \times \text{Height} + \text{Width} \times \text{Height}) \][/tex]
Given that the length is 8 inches, the width is 7 inches, and the lateral area is 150 square inches, we can substitute these values into the formula and solve for the height:
[tex]\[ 150 = 2 \times (8 \times \text{Height} + 7 \times \text{Height}) \][/tex]
[tex]\[ 150 = 2 \times (8\text{Height} + 7\text{Height}) \][/tex]
[tex]\[ 150 = 2 \times 15\text{Height} \][/tex]
Divide both sides by 2:
[tex]\[ 75 = 15\text{Height} \][/tex]
Now, solve for the height:
[tex]\[ \text{Height} = \frac{75}{15} \][/tex]
[tex]\[ \text{Height} = 5 \text{ inches} \][/tex]
So, the height of the rectangular prism is 5 inches.
6cm 20cm 4cm find the surface area
What is the LCD (Least Common Denominator) of 4 1/6 5 4/7?
Here are the steps to follow:
Find the Least Common Multiple of the denominators (which is called the Least Common Denominator).The LCD of [tex]\( \frac{4}{6} \)[/tex] and [tex]\( \frac{5}{7} \)[/tex] is [tex]42[/tex]. This is because [tex]42[/tex] is the smallest number that both [tex]6[/tex] and [tex]7[/tex] divide into evenly, ensuring that [tex]\( \frac{25}{6} \)[/tex] and [tex]\( \frac{39}{7} \)[/tex] can be expressed with a common denominator of [tex]42.[/tex]
1. Convert [tex]\( 4 \frac{1}{6}[/tex] to an improper fraction:
[tex]\[ 4 \frac{1}{6} = \frac{4 \times 6 + 1}{6} = \frac{24 + 1}{6} = \frac{25}{6} \][/tex]
2. Convert [tex]\( 5 \frac{4}{7} \)[/tex] to an improper fraction:
[tex]\[ 5 \frac{4}{7} = \frac{5 \times 7 + 4}{7} = \frac{35 + 4}{7} = \frac{39}{7} \][/tex]
Now, the fractions [tex]\( \frac{25}{6} \)[/tex] and [tex]\( \frac{39}{7} \)[/tex] need to have a common denominator to find the LCD.
Finding the Least Common Denominator (LCD)
To find the LCD, we need to determine the least common multiple (LCM) of the denominators [tex]6[/tex] and [tex]7[/tex]
The prime factorization of [tex]6[/tex] is [tex]\( 2 \times 3 \).[/tex]
The prime factorization of [tex]7[/tex] is [tex]\( 7 \).[/tex]
The LCM of [tex]6[/tex] and [tex]7[/tex] is [tex]\( 6 \times 7 = 42 \).[/tex]
Verify and Convert to Common Denominator:
Convert both fractions to have a denominator of [tex]42[/tex]
[tex]\[ \frac{25}{6} \times \frac{7}{7} = \frac{175}{42} \][/tex]
[tex]\[ \frac{39}{7} \times \frac{6}{6} = \frac{234}{42} \][/tex]
Now, [tex]\( \frac{25}{6} \) converts to \( \frac{175}{42} \) and \( \frac{39}{7} \) converts to \( \frac{234}{42} \).[/tex]
Please help with the second one. I can't figure it out!
Help with 2) show work
graham drove 42 1\3 miles in 1 1\3 hours how many hours did he take to drive one mile
The time taken by Graham is approximately 4/127 hours, which is about 0.0315 hours or roughly 1 minute and 53 seconds, to drive one mile.
To find out how many hours Graham took to drive one mile,
simply divide the total time (1 1/3 hours) by the total distance (42 1/3 miles):
Total time = 1 1/3 hours
= 4/3 hours
Total distance = 42 1/3 miles
= 127/3 miles
Now, divide the total time by the total distance:
Time per mile
= (Total time) / (Total distance)
= (4/3 hours) / (127/3 miles)
Now, when you divide by a fraction, you can multiply by its reciprocal:
Time per mile
= (4/3 hours) × (3/127 miles)
= (4/127) hours per mile
Therefore, the total time Graham took approximately 4/127 hours to drive one mile.
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When you buy a dozen bagels for $2.39 , you get an additional bagel free. What is your cost per bagel? (Round to the nearest cent.) Show your work.
If buying a dozen bagels for $2.39 also gets an additional bagel for free, the cost per bagel when rounded to the nearest cent is $0.18.
Explanation:The subject of your question is on the topic of unit cost. In this case, we will be calculating the cost per bagel when you buy a dozen bagels for $2.39 and get an additional bagel for free.
First, note that a dozen bagels means 12 bagels. But in this case, you get an extra bagel for free. So, you will have in total 13 bagels.Next, we divide the total cost by the total number of bagels to find the cost per bagel. That is, $2.39 divided by 13. When you do the calculation, you get approximately $0.184 per bagel.Since we need to round to the nearest cent, the final cost per bagel is $0.18 when rounded down.Learn more about Unit Cost here:https://brainly.com/question/29355214
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Write an expression for the calculation double the number 18 and then add 14 divided in half
What is the overlap of Data Set 1 and Data Set 2?
high
moderate
low
none
Answer:
There is moderate level of overlap between the two data sets.
Step-by-step explanation:
Overlap of data sets.
Overlap measures the degree of duplication that exists within data sets.It is an indicator of the degree to which data are identical.We are given two data sets in the question.
We have to find the amount of overlap in data set 1 and in data set 2.
There are 8 data points in data set 1 as shown in the image.
There are 8 data points in the data set 2 as shown in the image.
Out of the 8 data points for both data set 1 and data set 2, 5 data points overlap each other on 6, 7, 8 and 9.
Thus, we could say there is moderate level of overlap between the two data sets.
if 1 yard=3 feet and 1 mile=5,280 feet, how many yards are there in 2 miles
One side of a parallelogram is AB¯¯¯¯¯ . The height of the parallelogram is 3 units. The parallelogram has no right angles. Draw the parallelogram using the Polygon tool. Each segment on the grid represents 1 unit.
Answer:
Here
Step-by-step explanation:
i need help with 1, 2, 3, 7, 8, and 9! PLEASE HELP!
Two florist purchased flower bouquets and vases at the same store. The first florist bought 2 flower bouquets and 2 vases for a total of $12.50. The second florist bought 8 flower bouquets and 2 vases for a total of $29.00.
Let b represent the cost of one flower bouquet and v represent the cost of one vase. Write and solve a system of equations to find the price of each type of arrangement. Show all work.
We are given: The cost of one flower bouquet =$ b.
The cost of one vase = $ v.
First florist bought: 2 flower bouquets and 2 vases.
2 * cost of one flower bouquet + 2*cost of one vase = Total cost.
2b +2v = 12.50 ------------------------equation (1).
Second florist bought: 8 flower bouquets and 2 vases.
8 * cost of one flower bouquet + 2*cost of one vase = Total cost.
8b +2v = 29.00 ------------------------equation (2).
Therefore, system of equations we got is 2b +2v = 12.50 and 8b +2v = 29.00.
Subtracting first equation from second equation.
8b +2v = 29.00
-(2b +2v = 12.50)
____________________
6b = 16.50.
Dividing both sides by 6, we get.
b= 2.75.
Plugging b=2.75 in first equation we get
2(2.75) +2v = 12.50
5.50 +2v = 12.50
Subtracting 5.50 from both sides, we get
5.50-5.50 +2v = 12.50-5.50
2v = 7
Dividing both sides by 2, we get
v =3.50.
Therefore, cost of one flower bouquet is $2.75 and cost of one vase is $3.50.
the sweater shack is offering a 20% discount on sweaters. if the regular price of a sweater is 15.00 dollars what is the discount
The discount is $3.00 Why? You need to multiply the cost of the sweater by the discount as follows:
15x0.2=3